Electron acceleration by Alfven waves in the

magnetosphere

Peter Damiano and Jay Johnson Princeton Plasma Physics Laboratory

(image courtesy of NASA)

PPPL Theory Research and Review Seminar - Jan 23, 2015

Magnetosphere-Ionosphere Coupling

ou#low

Magnetosphere-Ionosphere Coupling

ou#lowMagnetospheric configuration changes drive Field Aligned Currents (FAC)

FAC

Magnetosphere-Ionosphere Coupling

ou#lowFACs carry electron flux into ionosphere

FAC

Electron flux interacts with atmospheric gases to produce aurora

Magnetosphere-Ionosphere Coupling

ou#lowPoynting and Electron flux also drive outflow of heavy ions

FAC

Which alters the magnetospheric configuration

• Monoenerge+c  Aurora  are  associated  with– quasi-‐sta+c  global  Field  Aligned  Currents– Low  frequency  Alfven  waves  

• Broadband  Aurora  are  associated  with– kine+c  scale  Alfven  waves  (λ⊥~c/ωpe,  ρs  or  ρi)  – and  can  drive  substan+al  ou#low

• Diffuse  Aurora– EMIC  and  whistler  waves  (radia+on  belts).

Auroral Morphology

Fundamental  Ques+ons:  •  How  and  where  are  e-‐  accelerated  to  carry  FACs?•  How  does  wave  energy  reach  dispersive  scales?•  How  do  auroral  arcs  form?  •  What  is  feedback  on  global  system?

Chaston  et  al.,  2008

R(*E(* 1%)(&&*)(S * 1) )*: &*8

+,-./#"0."(

91: ;')$4(# ??

()*+,

S"%-* 1)%)*'MC+L(#)(A TN

:%L( &*8(M!&JLU+*'N

QQ 8E

-" -.

*/-012

32*04(-"

35-/67245*QQ 8E

*)"A

(

35*/-012

89V&(')#$+ V+(#K5 B&"W%) C$+$-2/(#(

3%)*

-.%) C$+$-2/(#(ME:XE

Mono-energetic Aurora and low frequency Alfven waves

Field Line Resonance

xmxr

xt

xr xt xmx

VA(x)

ξx

Field Line Resonances (standing Alfven waves) and auroral arcs

FLRs  can  be  generated  by  mode  conversion  from  fast  mode

magnetopause  boundary

fast  mode

Long  extended  arc  in  azimuthal  direc+on  (out  of  page)

(Samson  et  al.,  2003)

(mHz  frequency  wave)

(Samson  et  al.,  2003)

Longitude 340o330o

La+tud

e

63o

66o

What generates E|| in Alfven waves?

•  Dispersive  wave  effects  -‐  (e.g.  Wei  et  al.,  1994;  Streltsov  and  Lotko  1996;  Bhaaacharjee,  et  al.  1999;  Wright  et  al.,  2002).

•  Anomalous  resis+vity    (Lysak  and  Dum,  1983;  Lotko  et  al.,  1998).

•  Mirror  force  effects  (Rankin  et  al.,  1999).

Ques+ons:   Can   we   generate   sufficient   E||   due   to   mirror   force  effects   in   a   self-‐consistent   kine+c   simula+on   to   accelerate  electrons  to  keV  energies?    What  are  signatures  of  accelera+on?

Need  E||  to  accelerate  trapped  electrons  to  carry  j||

Guiding center equations

Faraday’s Law

Momentum equation

Cold Plasma MHD equations

(Damiano et al., Phys. Plasmas, 14, 062904, 2007)

Perpendicular Ohm’s law

E? = �u�Bo

me

dv||dt

= �eE|| � µmr||Bo

h||dx||dt

= v||

�b��t

=�1

h||h�

�

�x||(h�E�)�

�

�x�(h||E||)

�

µo�o⇥u�⇥t

=Bo

h||h�

⇥

⇥x||(h�b�)

�

coupling via E|| (Gen. Ohm’s Law including moments of e- distribution function)

Particle/field interpolation done using standard PIC techniques.

2D hybrid MHD-kinetic electron model

x||x

x

mirror force term

Parallel (L=10)

iono

sphe

re

iono

sphe

re

Equator

Ionosphere

L=10

L=9.4

Perpendicular

Half-Gaussian results in only region of upward FAC

Ionospheric boundary at altitude of 1 Re

Initial Perturbation

Feedback in hybrid model • Perpendicular dispersion (S⊥=-‐E||bφ)•  Cross  scale  coupling

x||x

x

Plot northern hemisphere in dipolar coordinates

Field Aligned Current Density

Larger  Te  -‐>  increased  mirror  force  trapping  -‐>  remaining  current  carriers  must  be  accelerated  to  higher  velocity.

0.00 0.05 0.10 0.15 0.20 0.25time (TA)

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

elec

tron

ener

gy (k

eV)

0.0

0.2

0.4

0.6

0.8

1.0

Mirror force effects can accelerate electrons to keV energies

Te=200  eV

0.00 0.05 0.10 0.15 0.20 0.25time (seconds)

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

elec

tron

ener

gy (k

eV)

0.0

0.2

0.4

0.6

0.8

1.0

Te=keV

Electron acceleration is a large sink of wave energy

mono-energetic beam

Significant energy dissipation

Un-driven resonance would completely damp in < 2 TA -> same magnitude as Ohmic dissipation in ionospheric currents.

0 500 1000 1500 2000 2500e Δ Φ (eV)

-0.3

-0.2

-0.1

0

j 1 (µ

A/m

2 )

t=0.15 TA

0 500 1000 1500 2000 2500e Δ Φ (eV)

-0.3

-0.2

-0.1

0

j 1 (µ

A/m

2 )

t=0.2 TAt=0.25 TA

0.00 0.05 0.10 0.15 0.20 0.250.00.40.81.21.62.02.42.83.23.64.0

elec

tron

ener

gy (k

eV)

0.0

0.2

0.4

0.6

0.8

1.0

(a)

0.00 0.05 0.10 0.15 0.20 0.25time (TA)

0.0

0.2

0.4

0.6

0.8

1.0

Wav

e en

ergy

(nor

mal

ized

)

MHDTe=1000 eV

(b)

Te=keV

Broadband Aurora and Dispersive Alfven waves

Broadband  e-‐  precipita+on  correlated  with  Alfvenic  Poyn+ng  flux.

(Wing  et  al.,  2013) (Keiling  et  al.,  2003)

Broadband  electron  energy  flux Downward  Alfvenic  PoynIng  flux

Poyn+ng  flux  associated  with  ~Hz  frequency  dispersive  Alfven  waves  (λ||  ~  RE,  λ⊥  ~  λe,  ρs,  ρi).

Sun

Mo+va+on  -‐  Understanding  forma+on  of  Broadband  Aurora

Broadband aurora increase rapidly at onset (e.g. Wing et al., 2013).

Is dispersive scale structuring imposed at onset site or after?

Mo+va+on  -‐  Substorm  onset  and  Broadand  Aurora    

Understanding transit time of waves to ionosphere is important to help connect optical signatures to driving mechanism.

Wave observations (e.g. Lessard et al., 2006, Chi et al., 2009) used to evaluate onset timing and location.

Breaking  of  fast  flows  is  one  observed  source  of  KAWs

(Lessard et al., 2006, 2011)

Characteristics of wave-particle interactions depend on location

Fermi  accelera+on Par+cle  trapping

(Kletzing  et  al.,  1994)

(Waa

 and

 Rankin,  2010)

IAW  regime

 Path  along  field  line  is  a  highly  variable  plasma  environment

Alfven  wave KAW  regime

vth < VA

vth > VA

•    Loca+on/mechanism  for  accelera+on  not  clearly  established.•    Means  by  which  energy  reaches  dispersive  scales  not  known.•    Studies  to  date,  informa+ve  but  are  mostly  1D  or  local.  •    Limited  explora+on  of  ρi  effects  (Ti/Te  ~  7  in  plasma  sheet).

Faraday’s Law

Modified Momentum equation

Modified Perpendicular Ohm’s law

where

h||dx||dt

= v||

Hybrid gyrofluid-kinetic electron model in curvilinear coordinates

Cold Plasma MHD equations Guiding center equations

@b�

@t

=�1

h||h?

@

@x||(h?E?)�

@

@x?(h||E||)

�

me

dv||dt

= �eE|| � µmr||Bo

ũ� = (1� 1.25⇢2ir2?)u�

E? = �Bo(ũ� � ⇢2i

r2?ũ�)

x||x

x

coupling via E|| (Gen. Ohm’s Law including moments of e- distribution function)

(Damiano  et  al.,  Phys.  Plasmas,  14,    062904,    2007,    Cheng  and  Johnson,  1999,  Damiano  et  al.,  2015)

µ

o

⇢

o

@ũ

�

@t

=B

o

h||h�

@

@x||(h

�

b

�

)

�

perpendicular  E⊥  profile  at  equator

λ⊥~  0.1  RE

Identical pulses propagate to each field-aligned boundary (at 1 RE altitude above Earth surface).

Field line of maximum upward current

Kine+c  Alfven  wave  pulse  –  ini+al  perturba+on  example

Initialize KAW perturbation in the plasma sheet

9.4 9.6 9.8 10

ro (RE)

-10

-5

0

5

10

E⊥ (

mV

/m)

(b)

Two simulation cases: 1) Ti=0, Te=100 eV2) Ti=1 keV, Te=100 eV

k?k||

⇠ 10

k?k||

⇠ 10� 100 (Chaston et al., 2014)

 Increased  phase  speed,  but  reduced  coupling  

k?⇢i ⇠ 1

k?⇢i ⇠ 2

E||E?

=�k||k?⇢2s(1 + k2?⇢

2i )

Also evident in 2 fluid analysis(e.g. Chaston et al., 2003)

Hot Ion

Cold Ion

0 1 2 3 4 5 6 7 8l|| (RE)

-1

-0.5

0

j || / |

j ||m

ax (T

i=0)

|Ti=0, Te=100 eV

(a)Ti=1 keV, Te=100 eV

λ⊥eq=0.1 RE

0 1 2 3 4 5 6 7 8l|| (RE)

-1

-0.5

0

j || / |

j ||m

ax (T

i=0)

|

(b)

λ⊥eq=0.05 RE

t=8 s

! = k||VA

r1 + k2?⇢

2i (1 +

TeTi

)In plasma sheet, Te/Ti ~ 1/7

(Baumjohann et al., 1987)  

(e.g. Tatsuno et al., 2009)

!

k||= VA ⇠ 0.2⇥ 107m/s

Electron  distribu+on  func+on  evolu+on  

0 1 2 3 4 5 6 7 8 9 10l|| (RE)

0

0.5

1

1.5

2

2.5

3

V A (×

107

m/s

)

0 2 4 6 8 10l|| (RE)

-0.08

-0.06

-0.04

-0.02

0

j || (µ

A/m

2 )

Ti=0, t=30 sTi=1 keV, t=22 s

(a)

0 0.5 1 1.5|v⊥| (10

7 m/s)

-1.5

-1

-0.5

0

0.5

1

1.5

v || (1

07 m

/s)

t=30 s

(b)

0 0.5 1 1.5|v⊥| (10

7 m/s)

-1.5

-1

-0.5

0

0.5

1

1.5t=22 s

(c)

Parallel elongation in distribution function is qualitatively consistent with observations (e.g. Wygant, 2000) and simulations (Watt and Rankin, 2009)

Superposition at same l||=5 RE, but different times

More perpendicular dispersion for increased Ti

0 2 4 6 8 10l|| (RE)

-0.08

-0.06

-0.04

-0.02

0

j || (µA/m

2 )

Ti=0, t=30 sTi=1 keV, t=22 s

(a)

0.1 0.102 0.104 0.106x⊥

-0.08-0.06-0.04-0.02

00.020.040.060.08

j || (µA/m

2 )

l||=5 RE

(b)

Ionospheric  Evolu+on

0 5 10 15 20 25 30 35 40time (seconds)

-0.8

-0.6

-0.4

-0.2

0

j || (µA/m

2 )

Ti=0Ti=keV

(a)

0 0.5 1 1.5 2Energy (keV)

1

101

102

103

104

Ne

(b)

t=37 st=30 s

Broadband energization

ρi  effects  limit  current  and  electron  energiza+on  all  along  field  line  

• Mirror  force  effects  in  global  scale  Alfven  waves  self-‐consistently  produce  sufficient    ΔΦ||  to  accelerate  electrons  to  keV  energies  (consistent  with  observa+ons).  

• Electron  accelera+on  is  a  significant  sink  of  wave  energy.• Consistent  with  observa+ons,  electron  accelera+on  in  dispersive  

scale  Alfven  waves  is  broadband  in  nature

• ρi  effects  significantly  shorten  transit  +me  of  Alfven  wave  to  the  ionosphere  but  reduce  the  ability  of  the  wave  to  energize  electrons.

• E||  effects  (on  all  scales)  cause  a  perpendicular  dispersion  of  wave  energy.

Summary

• Mirror  force  effects  in  global  scale  Alfven  waves  self-‐consistently  produce  sufficient    ΔΦ||  to  accelerate  electrons  to  keV  energies  (consistent  with  observa+ons).  

• Electron  accelera+on  is  a  significant  sink  of  wave  energy.• Consistent  with  observa+ons,  electron  accelera+on  in  dispersive  

scale  Alfven  waves  is  broadband  in  nature

• ρi  effects  significantly  shorten  transit  +me  of  Alfven  wave  to  the  ionosphere  but  reduce  the  ability  of  the  wave  to  energize  electrons.

• E||  effects  (on  all  scales)  cause  a  perpendicular  dispersion  of  wave  energy.

Summary

Fundamental  Ques+ons:  •  How  and  where  are  e-‐  accelerated  to  carry  FACs?•  How  does  wave  energy  reach  dispersive  scales?  •  How  do  auroral  arcs  form?•  What  is  feedback  on  global  system?

• Broadband  aurora  -‐  parameter  study  (k⊥,  k||,  E⊥,Ti,  Te).• ρi  effects  on  Field  Line  Resonances  -‐  affects  E||  profile  (Streltsov  et  al.,  

1998)  -‐  observed  (Chaston  et  al.,  2013).• Fast  mode  dynamics  and  mode  conversion  (relevant  to  both  Field  Line  

Resonances  and  broadband  aurora)  -‐  stretched  tail  topologies  (MAG2D)  

• Ionospheric  coupling  -‐  (ionospheric  dissipa+on,  return  currents,  mul+-‐period  simula+ons    -‐>  auroral  arc  forma+on,  evolu+on)

• Cross-‐scale  coupling  of  wave  energy  [phase  mixing,  wave-‐wave  coupling  (nonlinear  MHD/3D),  wave  par+cle  interac+ons,  ionospheric  feedback].

• Nonlinear  sta+onary  iner+al  Alfven  waves  (nonlinear  MHD).• More  systema+c  comparison  with  satellite  observa+ons  (e.g  FAST,  Polar,  

Themis).

• More  realis+c  driving.

Future directions

Extra Slides

(plus    auxiliary  Poisson’s  equaIon  to  enforce  quasi-‐neutrality)

Moments  of  electron  distribuIon  funcIon  determined  from  kineIc  electrons  using  ParIcle-‐In-‐Cell  (PIC)  techniques.

(Damiano  et  al.,  Phys.  Plasmas,  14,    062904,    2007)

KAW

Mirror force terms

Generalized Ohm’s Law

@

@x?

h

�

h||h?

✓@(h||E||)

@x?

◆��

h||E||

�

2e

=@

@x?

✓h

�

h||h?

@

@x||(h?E?)

◆

+ eµo

@

@x||

Zv

2||fed

3v

+ µo

e

m

e

@B

o

@x||

Zµ

m

f

e

d

3v

� 2µo

e

m

e

@B

o

@x||

Zm

e

v

2||

2Bo

f

e

d

3v